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arXiv · hep-th/9304108

$q$-Deformed Classical Lie Algebras and their Anyonic Realization

Marialuisa Frau·Marco A. R-Monteiro·Stefano Sciuto
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Abstract

All classical Lie algebras can be realized à la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter $q$ is a phase related to the anyonic statistical parameter. A crucial rôle in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the underformed ones. The entire procedure works even on one dimensional chains; in such a case $q$ can also be real.

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Marialuisa Frau, Marco A. R-Monteiro, Stefano Sciuto. 1993-04-23. $q$-Deformed Classical Lie Algebras and their Anyonic Realization. https://doi.org/10.1088/0305-4470%2F27%2F3%2F022

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